Bottle cage? Just ride no-hands through the traffic with your hot coffee!
I used to do that at UC Davis in the early 80's. I'd pick up a cuppa at the Coffee House and head over to the Phy/Geo building, which entailed going through a big traffic circle in front of Chem 194. I'd head into the traffic circle with my coffee in my hand, riding no-hands, and watch the freshmen just scatter out of the way. 270 degrees through the roundabout, and on my way!